Magnetic field sensors are used in a variety of applications, including, but not limited to, an angle sensor that senses an angle of a direction of a magnetic field, a current sensor that senses a magnetic field generated by a current carried by a current-carrying conductor, a magnetic switch that senses the proximity of a ferromagnetic object, a rotation detector that senses passing ferromagnetic articles, for example, magnetic domains of a ring magnet or a ferromagnetic target (e.g., gear teeth) where the magnetic field sensor is used in combination with a back-biased or other magnet, and a magnetic field sensor that senses a magnetic field density of a magnetic field.
Various parameters characterize the performance of magnetic field sensors and magnetic field sensing elements. With regard to magnetic field sensing elements, the parameters include sensitivity, which is the change in the output signal of a magnetic field sensing element in response to a magnetic field, and linearity, which is the degree to which the output signal of a magnetic field sensor varies linearly (i.e., in direct proportion) to the magnetic field.
Some magnetic field sensors include magnetoresistance (MR) elements, such as giant magnetoresistance (GMR) elements and tunneling magnetoresistance (TMR). Generally, GMR and TMR elements have a relatively high sensitivity compared, for example, to Hall effect elements. GMR and TMR elements have moderately good linearity, but over a restricted range of magnetic fields. However, even in the restricted range of magnetic fields, the linearity of the GMR or TMR element can suffer from irregularities, such as due to high temperatures.
Further, angle sensors using GMR and TMR elements can experience angle error due to phenomena such as spin flop (i.e., alteration of reference direction at high magnetic fields or anisotropy field (e.g., magnetocrystalline anisotropy or shape anisotropy)). For example, the angle obtained with GMR elements can experience error up to several degrees.